Lab2_report

Paul Dolphyne Ackah Physics 201 Lab 2 Report – Microwave Polarization and Interferometer Introduction This lab delves into the realm of microwaves, which are a subset of electromagnetic waves characterized by wavelengths ranging from 1 millimeter to 1 meter. Microwaves serve various purposes, including communication and weather prediction. The primary objectives of this experiment are twofold: to study the influence of linear polarization angles on microwave reception and to construct a microwave Michelson interferometer, comparing the obtained values with theoretical ones. Maxwell's equations provide the wave equations for electric and magnetic fields, elucidating the various polarizations of electromagnetic waves. Vertical polarization involves electric waves oscillating solely in the vertical plane, leading to a horizontally oscillating magnetic field. Additionally, electromagnetic radiation can exhibit circular or elliptical polarization, generating a helix-like, circularly polarized electric field. The Michelson-Morley experiment, originally designed to detect changes in the speed of light attributed to Earth's motion through a theoretical "luminiferous aether," laid the foundation for the Lorentz-Fitzgerald transformations by revealing no such variations in the speed of light. In this lab, we recreate a similar experiment using microwaves instead of visible light.

Procedure The experiment unfolds in four parts. In the first segment, we employ a microwave transmitter and receiver alongside a goniometer. Placing the transmitter and receiver opposite each other, we systematically adjust the receiver's angle in 10-degree increments, recording signal strength at each setting. In the second part, a polarizing filter is introduced between the transmitter and receiver, with the receiver initially set at 0 degrees. We rotate the polarizing filter in 22.5-degree increments, documenting signal strength as we go. The third experiment involves setting the receiver at 90 degrees, producing zero signal. Here, we once again incorporate the polarizing filter, rotating it in 45-degree increments while recording signal strengths. In the fourth and final part, we assemble a Michelson interferometer akin to the one utilized in the Michelson-Morley experiment. This setup entails two microwave reflectors, a partial reflector, and a microwave transmitter and receiver. One of the reflectors is systematically moved away from the detector until it completes 10 cycles of minima and maxima, enabling us to calculate our measured wavelength value. Data Experiment 1 (no polarizing filter) Detector Angle (degrees) Signal Level (mA) -90 0.6 -80 3.6 -70 8.4 -60 13.2

Polarizer Angle Signal Level (mA) 0 (horizontal) 27 22.5 12 45 21.6 67.5 3 90 (vertical) 6 Graph 2. Polarizer angle vs. cos(θ), cos 2 (θ), signal level in mA Experiment 3 (receiver set at 90 degrees) Graph 3. Polarizer angle vs. cos(θ), cos2(θ), signal level in mA Experiment 4 (Michelson interferometer) Initial reflector location: 27 cm Final reflector location: 12.5 cm -10 0 10 20 30 0 22.5 45 67.5 90 cos(θ), cos2(θ), signal level ( ) mA Polarizer Angle (degrees) Experiment 2 cos(θ) cos2(θ) signal level -50 0 50 100 Polarizer Angle cos(θ) cos2(θ) signal level cos(θ), cos2(θ), signal level (mA) Polarizer Angle (degrees) Experiment 3 Series1 Series2 Series3 Polarizer Angle Signal Level (mA) 0 (horizontal) 0 45 11.7 90 (vertical) 0

Calculation and Error Analysis Given that the reflector traveled through 10 minima, its total displacement corresponds to five times the wavelength. Therefore, we can calculate our observed wavelength by finding the difference between the initial and final reflector positions and dividing this difference by 5. 27 cm – 12.5 cm = 14.5 cm Wavelength: 14.5 cm / 5 = 2.90 cm Percent error: the theoretical value is 2.85 centimeters. This gives us an error of 1.75%. 𝑒𝑟𝑟𝑜𝑟 1.75% ’()’"#’* +./0 The margin of error can be considered negligible, considering the manual adjustment of the reflector's position and the estimation of measurements by eye. Given the inherent potential for discrepancies in these manual processes, a percent error below 2% is deemed acceptable and satisfactory for this laboratory experiment.

In summary, this laboratory experience provided us with valuable insights into microwaves, particularly their polarization characteristics, and afforded us the opportunity to replicate a classic experiment – the Michelson-Morley experiment – using microwaves. The results closely aligned with theoretical values and imparted practical, hands-on experience in working with electromagnetic waves and interferometry. Pre-Lab Questions 1. If the detector readings are proportional to the amplitude of the microwave E field, the data from the first polarization experiment should be proportional to cos(θ) where θ is the angle between transmitter and detector. If the readings are proportional to the energy stored in the E field, the readings should be proportional to cos 2 (θ). Based on your data, are the detector readings proportional to amplitude, energy, or neither? The readings obtained from the detector exhibit a direct proportionality to energy. As evident in graph 1, these readings display a direct proportionality to cos^2(θ), thereby affirming the direct relationship between the readings and energy. 2. The simplest design for a radio/microwave transmitter antenna is a vertical conducting rod about one quarter-wavelength long. A mobile-phone manufacturer wants to build such an antenna into a GSM-900 (900 MHz) phone. How small can the phone be?

The calculation of wavelength involves dividing the speed of light by the frequency. With the provided frequency of 900 MHz, the resulting wavelength equals 0.33 meters. To obtain the length of a quarter-wavelength rod, we divide this value by four, yielding a length of 8.3 centimeters. 3. For aerodynamic reasons, nearly all modern aircraft feature at least one large vertical stabilizer. The B-2 “stealth” bomber pictured to the right, however, has no vertical fins at all. Why not? The aircraft depicted is a stealth bomber, and the addition of a sizable fin could potentially elevate the risk of radar detection, thereby compromising its intended stealth capabilities and jeopardizing its safety. It's worth noting that a stealth aircraft of this nature may not require a conventional stabilizer, as its operational profile extends beyond mere flat turns. 4. TV stations in the U.S. normally broadcast horizontally-polarized signals. Is this TV antenna mounted correctly, or should it be rotated? Signals typically have horizontal polarization, and therefore, the antenna achieves optimal signal reception when mounted in a horizontal orientation. No correction is necessary in this regard.